结合模态区间分析和IARR的不确定性损伤识别  

Uncertainty-Based Damage Identification Using Modal Interval Analysis and Improved Analytical Redundancy Reduction

作　　者：方圣恩[1,2] 张宝[1] FANG Shengen;ZHANG Bao(School of Civil Engineering,Fuzhou University Fuzhou,350108,China;National and Local United Research Center for Seismic and Disaster Informatization of Civil Engineering,Fuzhou University Fuzhou,350108,China)

机构地区：[1]福州大学土木工程学院,福州350108 [2]福州大学土木工程防震减灾信息化国家地方联合工程研究中心,福州350108

出　　处：《振动．测试与诊断》2019年第4期810-815,907,共7页Journal of Vibration,Measurement & Diagnosis

基　　金：国家自然科学基金资助项目(51578158);福州大学“旗山学者”奖励支持计划资助项目(GXRC-1688)

摘　　要：针对结构不确定性损伤识别中经典区间算法容易发生扩张的问题,提出将模态区间分析和改进解析冗余度(improved analytical redundancy reduction,简称IARR)相结合的损伤识别方法。首先,将结构静力平衡方程用约束条件方程组表示,通过改进解析冗余度使得方程组仅包含平动变量;其次,把与假定损伤单元相关的方程集中在同一子集,代入区间变量将方程扩展成区间形式,通过模态区间运算判断各约束条件的满足情况来实现损伤定位;最后,采用静载作用下的试验钢梁验证所提出的方法,结合刚度参数、挠度参数和外荷载3种随机变量,建立各梁段约束条件方程。结果表明:考虑测试误差、参数不确定性时,能通过约束条件的不满足有效定位梁的小损伤。In order to solve the easy overestimation of classic interval algorithms for uncertainty-based damage identification of structures,an identification method is developed incorporating modal interval analysis with improved analytical redundancy reduction(IARR).Firstly the equations of structural static equilibrium are replaced by a set of constraint equations.Then the proposed improved analytical redundancy reduction algorithm is used to eliminate the rotation variables in the equations and most important of all,to make the equations related to damage components stay in the same subset.After that,the equations are expanded to interval format through adopting interval variables.Modal interval analysis is executed to evaluate the satisfaction of each constraint equation,by which means damage can be located.An experimental steel beam under a static load is used to validate the proposed method.The constraint equations for each beam segment are established based on three random parameters related to the stiffness,the deflections and the load.The analysis results demonstrate that taking into account the test error and parameter uncertainties,the proposed method can effectively locate the minor damage according to the unsatisfied constraints.

关 键 词：不确定性损伤识别 模态区间分析 改进解析冗余度 约束满足问题 钢梁试验 

分 类 号：O327[理学—一般力学与力学基础] TU311[理学—力学]